What exactly happened during Reagan's invocation of the 25th Amendment?

Question

I was reading the Wikipedia article on the 25th Amendment when I came across this confusing paragraph (I bolded the sections of interest):

Fielding and White House Chief of Staff Donald Regan recommended that Reagan transfer power and two letters doing so were drafted: the first letter specifically invoked Section 3 of the Twenty-fifth Amendment; the second only mentioned that Reagan was mindful of this provision. At 10:32 a.m. on July 13, Reagan signed the second letter and ordered its delivery to the appropriate officers as required under the amendment. Vice President George H. W. Bush was Acting President from 11:28 a.m. until 7:22 p.m., when Reagan transmitted a second letter to resume the powers and duties of the office. It is the longest "term" as Acting President and makes George H.W. Bush the person to serve as Acting President for the longest cumulative time.

1. Is that the second or the third letter? A "second" letter was already ordered at 10:32 a.m. to be delivered, so how could this "second" letter be transmitted at 7:22 p.m.? Are they talking about the same letter?
2. Is that really the longest term of an Acting President? What happened, when, say, Lincoln was assassinated?

Answer 1

Vice President George H. W. Bush was Acting President from 11:28 a.m. until 7:22 p.m., when Reagan transmitted a second letter to resume the powers and duties of the office.

You are correct. This is a third letter. Two were prepared previously and one was thrown away. This sentence would make more sense if it read "another" or "a followup" rather than "a second" letter. This is confusing rather than incorrect though. It was the second letter that was actually sent, although it was the third prepared. That's evident just from the section that you posted.

Is that really the longest term of an Acting President? What happened, when, say, Lincoln was assassinated?

Prior to the twenty-fifth amendment, which was ratified on February 10th of 1967, there was no acting president. John Tyler set the precedent in that. There was an argument that he was acting president after William Henry Harrison died. Tyler insisted that he was actually president. Subsequently Tyler's view was confirmed. So until 1967, there was no such thing as an acting president.

Specifically with Abraham Lincoln, Lincoln was president. Then he was shot. Then he died. Then Andrew Johnson took the oath of office. Then Johnson was president. So there was never an acting president term. Lincoln was president until he wasn't. If he had lingered in a coma, Johnson might have been effectively president. Or not. That's why the 25th amendment exists, to avoid these ambiguous situations. So people wouldn't have felt a need to hold out for a Lincoln recovery in that hypothetical situation.

In 1985, George H. W. Bush became the first acting president ever, for more than seven hours. Since then, Dick Cheney became acting president twice. Both times, George W. Bush had no complications and resumed his duties in less than three hours.

Presumably the second Bush was only invoking as a precaution. If something happened and he was not able to resume duties, the cabinet would not have needed to invoke section 4 to note his incapacitation. He could have gone straight to surgery, confident that things were being handled. Note that Reagan had to invoke after the same procedure. So if Bush had followed Reagan's precedent, he wouldn't have invoked at all.

George H. W. Bush is one of only two acting presidents for three terms between them. Of those three instances, Bush's term was the longest by more than five hours.

Answer 2

@Brythan had a good answer about the situation, but the term "Acting [insert job title]" comes up frequently in the United States government. You can see a good example of this in fiction in Star Trek TNG (which is heavily based on U.S. government (specifically U.S. Navy) in terms). Consider every time Riker is in charge of the bridge (and usually Picard is off ship) and the pissed off alien calls, he introduces himself as "Acting Captain" in a similar manner. Typically it denotes that the person is not the full time holder of the position, but the person who does hold the position is not available (be it that they are on leave or scheduled off duty, or they cannot be contacted). In other cases, it could denote that the position has not been filled and the deputy officer is fulfilling those duties until the position can is filled. This isn't always snubbing the deputy as they may not have the rank to fill the office full time, but can do the job until it comes back. This case doesn't apply to the President as the Constitution specifically says that the Vice President takes over (well... not really... we'll get to that in a moment).

An Acting President in the modern U.S. Government only occurs when the President is taking a temporary leave of absences and anticipates returning to full duty later. As mentioned above, thus far, all three times were in relation to surgery and specifically when the President was anesthetized for the surgery. This became important during the cold war because only the President of the United States is authorized to launch a nuclear strike and congress didn't want the President to be out cold with inbound missiles (most of the 25th amendment is for extreme emergencies so that there is always a Person who is President). As stated, the President permanently leaving office premature of election makes the next eligible person in line President.

Surprisingly, while the 25th Amendment is new, but the problem it sought to fix is quite old. As written the constitution says that the Vice President takes over the role if the President cannot, but doesn't actually say he becomes President. When the first President to die in office ("William Henry Harisson, how do you praise/ that guy was dead in 30 days!" for all you Animaniacs fans out there. And yes, he was dead after 30 days in office... from Pneumonia he caught during his inauguration) there was much confusion as to whether John Tyler (his Veep turned President) was to be addressed as Vice President, Acting President, or President that went on until Tyler said, "I'm President John Tyler" and everyone shut up. So, you're certainly not wrong in thinking that the Vice President would become Acting President as there was some drama about the issue. On the flip side, there are some people who think that it's better to refer to Gerald Ford as "Acting President Ford" due to a combination of reasons, both that he was never elected (the elected veep stepped down prior to Nixon's resignation... for a wholly different scandal than Watergate) and Ford (then Senate Minority Leader) was pushed by the Speaker of the House Carl Albert in secret (a Democrat) because he did not want Nixon's likely impeachment to lose Republican support because it looked like it was Coup on his part (Albert was second in line for Presidency with no Veep in place). Additionally, and more a dig, Ford acted more like an Acting President than a President (i.e. Ford's policies were minimal and his role more ceremonial than previous ascended Vice Presidents, especially Johnson. Or if you want it to be said in a less pleasant way, Ford was keeping the seat warm for the next guy who was elected... and all but securing that next guy was going to be any Democrat with a pulse, (which is probably the most agreeable thing one can say about Cater) due to his general unpopularity).